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Simulation of ‘hitch-hiking’ genealogies. (English) Zbl 0981.92020

Summary: An ancestrial influence graph is derived, an analogue of the coalescent and a composite of R.C. Griffiths’ [IMS Lect. Notes, Monogr. Ser. 18, 100-117 (1991; Zbl 0781.92022)] two-locus ancestral graph and S.M. Krone and C. Neuhauser’s [Theor. Popul. Biol. 51, No. 3, 210-237 (1997; Zbl 0910.92024)] ancestral selection graph. This generalizes their use of branching-coalescing random graphs so as to incorporte both selection and recombination into gene genealogies. Qualitative understanding of a ‘hitch-hiking’ effect on genealogies is pursued via diagrammatic representation of the genealogical process in a two-locus, two-allele haploid model.

Extending the simulation technique of R.C. Griffiths and S. Tavaré [Math. Comput. Modelling 23, No. 8-9, 141-158 (1996; Zbl 0853.92014)], computational estimations of expected times to the most recent common ancestor of samples of $n$ genes under recombination and selection in two-locus, two-allele haploid and diploid models are presented. Such times are conditional on sample configuration. Monte Carlo simulations show that ‘hitch-hiking’ is a subtle effect that alters the conditional expected depth of the genealogy at the linked neutral locus depending on a mutation-selection-recombination balance.

##### MSC:
 92D15 Problems related to evolution 92D10 Genetics 05C90 Applications of graph theory